Former Lib Dem town hall leader Terry Stacy has called for the plaque to be installed at the former Wessex Sound Studios building in Highbury New Park, where the Clash recorded London Calling.
The petition calls on Islington Council to fund the plaque and freeholder Church Pastoral Aid to consent to it being added to the building, which has been converted into luxury apartments.
Islington Council says it would be "great" to have a plaque at the studio and is looking into it.
The former church hall, part hidden behind St Augustines Church, was bought by The Beatles director Sir George Martin in 1965 and converted into the Wessex Sound Studios.
As well as the Clash and The Beatles, it went on to be graced by musical heavyweights such as Queen, The Rolling Stones and Sex Pistols.
The petition states: "London Calling the historic album by the Clash, that rocked the music scene, should be formally commemorated with an Islington Council green plaque.
"The groundbreaking London Calling was an album that changed the music scene forty years ago, serving as an anthem for London, Londoners and music lovers globally. [...]
"So, 40 years after the album was released we feel that it should be commemorated."
The petition had more than 300 signatures at the time we went to print. Terry said he started the Islington Green Plaque scheme during his stint as council leader and unveiled memorial plaques for the actors Alexander McQueen and comedy writer Kenneth Williams, who both had links to the borough. Asked why the former studio deserves the fuss, Terry told the Gazette: "I'm a great local history buff. I'm a secret Clash fan. It's around the corner.
"London Calling was a defining album used in the Olympics and the Clash are a world renowned band. Why shouldn't we commemorate it?"
He added: "I think it's a great opportunity to commemorate this landmark building, most people don't know it's there.
"London's Calling is a melting pot of musical styles but one thing I always thought the Clash did very well was there was always an underlying passion and desire for social justice it.
"That was a period of social change - it happened in Highbury and it needs to be put on the tourist trail."
Terry says he'd even start a crowdfunding campaign to cover the costs if Islington Council says it can't afford the plaque.
Islington's business chief Cllr Asima Shaikh said: "Islington Council has a very strong track record in celebrating the people and history of our borough, such as with our popular Heritage Plaques and People's Plaques.
"We're currently working, for example, on unveiling a plaque later this spring commemorating the author Andrea Levy, who was born and grew up in Islington.
"This studio was famous for a number of recordings, including The Clash's London Calling. It would be great to have this celebrated and we will look at how we may be able to support a plaque for this location."
In 2013 the studio was nominated for a plaque, but wasn't chosen as another option received more support in the popular vote
London Calling was the Clash's third album. From the famous chords of the title track, to the deep dub of Guns of Brixton and the light singalong of Train In Vain, it was the sound of a band having fun experimenting with different forms of pop music.
The classic lineup of frontman Joe Strummer, lead guitarist Mick Jones, bass guitarist Paul Simonon and drummer Topper Headon spent just a month or so in the studio, putting together what became their first double album. Recording began in August 1979, with producer Guy Stevens, and the record was released in December 1979, reaching number nine in the UK charts and going on to sell millions around the world. The Museum of London currently has a free exhibition The Clash - London Calling from 10am to 6pm daily until April 19, where visitors can see gems like Joe Strummer's original notes and the band members' instruments.
You can view the petition here: change.org/p/islington-council-church-pastoral-aid-trust-plaque-call-for-site-clash-s-historic-album-london-s-calling-was-recorded/u/25716758
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